We construct a categorification of the modular data associated with every family of unipotent characters of the spetsial complex reflection group $G(d,1,n)$. The construction of the category follows the decomposition of the Fourier matrix as a Kronecker tensor product of exterior powers of the character table S of the cyclic group of order d. The representations of the quantum universal enveloping algebra of the general linear Lie algebra ${\mathfrak{gl}}_m$, with quantum parameter an even root of unity of order 2d, provide a categorical interpretation of the matrix ${\bigwedge }^{m}S$. We also prove some positivity conjectures of Cuntz at the decategorified level.

中文翻译：

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来自量子一般线性群的 G(d,1,n) 的傅立叶矩阵

我们构建了与特殊复合反射群的每个单能特征家族相关的模块化数据的分类 $G(d,1,n)$. 类别的构造遵循傅立叶矩阵分解为d阶循环群的字符表S的外部幂的 Kronecker 张量积。一般线性李代数的量子普适包络代数的表示${\mathfrak{高尔}}_{米}$, 量子参数是 2 d阶统一的偶数根, 提供矩阵的分类解释${\bigwedge }^{米}秒$. 我们还证明了 Cuntz 在非分类层面的一些积极性猜想。